partial commit in static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / fsle_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/fsle_drops.ma b/matita/matita/contribs/lambdadelta/static_2/static/fsle_drops.ma
index 5d72ba39b69009f7b683c830c991f5a6d63e2a1f..87d3864ffe6c48f1d331e78242f61706d73c596b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/fsle_drops.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/fsle_drops.ma
@@ -19,7 +19,7 @@ include "static_2/static/fsle_length.ma".
 
 (* Advanced properties ******************************************************)
 
-lemma fsle_lifts_sn: ∀T1,U1. ⇧*[1] T1 ≘ U1 → ∀L1,L2. |L2| ≤ |L1| →
+lemma fsle_lifts_sn: ∀T1,U1. ⇧[1] T1 ≘ U1 → ∀L1,L2. |L2| ≤ |L1| →
                      ∀T2. ❪L1,T1❫ ⊆ ❪L2,T2❫ → ❪L1.ⓧ,U1❫ ⊆ ❪L2,T2❫.
 #T1 #U1 #HTU1 #L1 #L2 #H1L #T2
 * #n #m #f #g #Hf #Hg #H2L #Hfg
@@ -30,7 +30,7 @@ lapply (frees_lifts_SO (Ⓣ) (L1.ⓧ) … HTU1 … Hf)
 qed-.
 
 lemma fsle_lifts_dx (L1) (L2):
-                    |L1| ≤ |L2| → ∀T2,U2. ⇧*[1]T2 ≘ U2 →
+                    |L1| ≤ |L2| → ∀T2,U2. ⇧[1]T2 ≘ U2 →
                     ∀T1. ❪L1,T1❫ ⊆ ❪L2,T2❫ → ❪L1,T1❫ ⊆ ❪L2.ⓧ,U2❫.
 #L1 #L2 #HL21 #T2 #U2 #HTU2 #T1
 * #n #m #f #g #Hf #Hg #H2L #Hfg
@@ -41,36 +41,36 @@ lapply (frees_lifts_SO (Ⓣ) (L2.ⓧ) … HTU2 … Hg)
 qed-.
 
 lemma fsle_lifts_SO_sn: ∀K1,K2. |K1| = |K2| → ∀V1,V2. ❪K1,V1❫ ⊆ ❪K2,V2❫ →
-                        ∀W1. ⇧*[1] V1 ≘ W1 → ∀I1,I2. ❪K1.ⓘ[I1],W1❫ ⊆ ❪K2.ⓑ[I2]V2,#O❫.
+                        ∀W1. ⇧[1] V1 ≘ W1 → ∀I1,I2. ❪K1.ⓘ[I1],W1❫ ⊆ ❪K2.ⓑ[I2]V2,#O❫.
 #K1 #K2 #HK #V1 #V2
 * #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HK12 #Hf12
 #W1 #HVW1 #I1 #I2
 elim (lveq_inj_length … HK12) // -HK #H1 #H2 destruct
-/5 width=12 by frees_lifts_SO, frees_pair, drops_refl, drops_drop, lveq_bind, sle_weak, ex4_4_intro/
+/5 width=12 by frees_lifts_SO, frees_pair, drops_refl, drops_drop, lveq_bind, pr_sle_weak, ex4_4_intro/
 qed.
 
 lemma fsle_lifts_SO: ∀K1,K2. |K1| = |K2| → ∀T1,T2. ❪K1,T1❫ ⊆ ❪K2,T2❫ →
-                     ∀U1,U2. ⇧*[1] T1 ≘ U1 → ⇧*[1] T2 ≘ U2 →
+                     ∀U1,U2. ⇧[1] T1 ≘ U1 → ⇧[1] T2 ≘ U2 →
                      ∀I1,I2.  ❪K1.ⓘ[I1],U1❫ ⊆ ❪K2.ⓘ[I2],U2❫.
 #K1 #K2 #HK #T1 #T2
 * #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HK12 #Hf12
 #U1 #U2 #HTU1 #HTU2 #I1 #I2
 elim (lveq_inj_length … HK12) // -HK #H1 #H2 destruct
-/5 width=12 by frees_lifts_SO, drops_refl, drops_drop, lveq_bind, sle_push, ex4_4_intro/
+/5 width=12 by frees_lifts_SO, drops_refl, drops_drop, lveq_bind, pr_sle_push, ex4_4_intro/
 qed.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma fsle_inv_lifts_sn: ∀T1,U1. ⇧*[1] T1 ≘ U1 →
+lemma fsle_inv_lifts_sn: ∀T1,U1. ⇧[1] T1 ≘ U1 →
                          ∀I1,I2,L1,L2,V1,V2,U2. ❪L1.ⓑ[I1]V1,U1❫ ⊆ ❪L2.ⓑ[I2]V2,U2❫ →
                          ∀p. ❪L1,T1❫ ⊆ ❪L2,ⓑ[p,I2]V2.U2❫.
 #T1 #U1 #HTU1 #I1 #I2 #L1 #L2 #V1 #V2 #U2
 * #n #m #f2 #g2 #Hf2 #Hg2 #HL #Hfg2 #p
 elim (lveq_inv_pair_pair … HL) -HL #HL #H1 #H2 destruct
 elim (frees_total L2 V2) #g1 #Hg1
-elim (sor_isfin_ex g1 (⫱g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
+elim (pr_sor_isf_bi g1 (⫰g2)) /3 width=3 by frees_fwd_isfin, pr_isf_tl/ #g #Hg #_
 lapply (frees_inv_lifts_SO (Ⓣ) … Hf2 … HTU1)
 [1,2: /3 width=4 by drops_refl, drops_drop/ ] -U1 #Hf2
-lapply (sor_inv_sle_dx … Hg) #H0g
-/5 width=10 by frees_bind, sle_tl, sle_trans, ex4_4_intro/
+lapply (pr_sor_inv_sle_dx … Hg) #H0g
+/5 width=10 by frees_bind, pr_sle_tl, pr_sle_trans, ex4_4_intro/
 qed-.